Coherent control of localization in driven quasicrystals and integer quantum Hall systems*

We report experimental and theoretical advances in coherent control of a localization quantum phase transition in a shaken quasicrystal. By controlling the amplitude and phasonic/phononic character of modulation applied to atoms in an 1D bichromatic optical lattice, we experimentally observe the competition between dynamical and Anderson localization and demonstrate coherent tuning of the localization transition. We elucidate the mapping between this system and a two-dimensional integer quantum Hall system, in which our modulation protocol maps to light with fully tunable polarization. We discuss two possibilities illuminated by this higher-dimensional mapping: engineering a thermodynamically stable critical phase hosting multifractal wave functions, and modifying topological properties.